# Calculating the inertia tensor for an articulated character

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I've been struggling to figure out how to compute the angular momentum of my character and I am stuck at calculating the mass matrix tensor. I was hoping that one of the kind souls on this forum would point me in the right direction.

From the paper I am reading I cannot figure out what the variable x[sub]j[/sub] represents in the equation for the inertia tensor;

[attachment=5379:inertia_tensor.gif]

and it does not help that I am still generally confused about the formulas... In any case, M[sub]i[/sub] represent the inertia tensor matrix for the i'th body part and m[sub]i[/sub] the mass of that body part.

To be specific, I am wondering what you think that equation suggests I should be using as values for x[sub]j[/sub], center of mass for the individual body parts? Does it treat the body part as a particle with a certain mass or as a volume?

I do not expect anyone to read through the entire paper - I'll of course provide any clarifications/elaborations, but, If you still wish to take a look the paper can be found here;
with the equation in question at page 8.

Cheers!

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So, not too many replies yet

Well, let's try something else then - the body that I am trying to calculate the [color="#1C2837"]angular momentum for is a compound of a set of body parts. Since I have the center of mass and the mass of each individual body part,[font="sans-serif"] will it yield the same result[/font][color="#1C2837"] if I treat the body parts as particles as opposed to, say, [font="sans-serif"]cuboids so long as the mass and center of mass is the same?[/font]

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So, not too many replies yet

Well, let's try something else then - the body that I am trying to calculate the [color="#1C2837"]angular momentum for is a compound of a set of body parts. Since I have the center of mass and the mass of each individual body part,[font="sans-serif"] will it yield the same result[/font][color="#1C2837"] if I treat the body parts as particles as opposed to, say, [font="sans-serif"]cuboids so long as the mass and center of mass is the same?[/font]

That's an easy question: No, it will not be the same. Just think of a trivial example with a single body part, and you'll see the center of mass and the mass just don't encode enough information to compute the moment of inertia. The result you get might be good enough for a game, but in general you probably need to know that moment of inertia of each body part and use the parallel axis theorem.

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That's an easy question: No, it will not be the same. Just think of a trivial example with a single body part, and you'll see the center of mass and the mass just don't encode enough information to compute the moment of inertia. The result you get might be good enough for a game, but in general you probably need to know that moment of inertia of each body part and use the parallel axis theorem.

That makes sense of course. I think I will try to get it working with the particle method and maybe then look into the parallel axis theorem. Rotating the tensor is something like R*I*R^transposed as I've understood it... Great, thanks a lot!

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